MathematicsWhich of the following is the value of 1 7 + 3 − 2  ?

Which of the following is the value of 1 7 + 3 2  ?


  1. A
      3 7 4 2 + 42 10  
  2. B
      3 3 7 4 2 + 42 10  
  3. C
      3 3 7 +4 2 + 42 10  
  4. D
      3 3 + 7 +4 2 + 42 10   

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    Solution:

    Consider the given question,
    1 7 + 3 2  
    The conjugate of the denominator is,
    ( 7 + 3 ) 2 =( 7 + 3 )+ 2  
    Rationalizing,
    1 7 + 3 2 × ( 7 + 3 )+ 2 ( 7 + 3 )+ 2  
    We know that,
    (ab)(a+b)= a 2 b 2  
    Then,
    Again rationalizing,
    ( 7 + 3 )+ 2 ( 7 + 3 ) 2 ( 2 ) 2 = 7 + 3 + 2 2(4+ 21 ) × 4 21 4 21  
    Applying identity (ab)(a+b)= a 2 b 2  ,
    ( 7 + 3 )+ 2 ( 7 + 3 ) 2 ( 2 ) 2 = 4 7 3×7×7 +4 3 3×3×7 +4 2 42 2 (4) 2 ( 21 ) 2  
    Simplifying,
    Hence, the value of  1 7 + 3 2  is   3 3 7 4 2 + 42 10  .
    Therefore, option 2 is correct.
     
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